# Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling

## TL;DR

This paper introduces a unifying framework for constructing nodal-point semimetals with tunable dispersions, providing a new perturbative approach to study strongly interacting non-Dirac semimetals and their quantum critical behaviors.

## Contribution

It presents a general scheme to classify and analyze semimetals with different dispersing directions, enabling exploration of strong coupling phenomena in non-Dirac systems.

## Key findings

- Identified a new perturbative route to access strongly interacting semimetals.
- Analyzed quantum critical phenomena and non-Fermi liquid states using an epsilon expansion.
- Related theoretical models to real materials like strained optical honeycomb lattices.

## Abstract

We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with $d_Q>0$. As a demonstrative example, we relate a two dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological transition between a Dirac semimetal and a normal insulator, and its three dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quantum critical phenomena and emergence of non-Fermi liquid states with unusual dynamical structures within the framework of an $\epsilon$ expansion, where $\epsilon=2-d_Q$, when these systems reside at the brink of charge- or spin-density-wave orderings, or an $s$-wave pairing. Our results can be germane to two-dimensional uniaxially strained optical honeymcomb lattice, $\alpha$-(BEDT-TTF)$_2\text{I}_3$.